SQA Advanced Higher Mathematics Methods in Algebra and Calculus overview quiz quiz

Nothing, it is already proper

Divide, because it is improper

Factorise the numerator

Complete the square

$\dfrac{A}{x - 1} + \dfrac{B}{x + 3}$

$\dfrac{A}{(x - 1)^2} + \dfrac{B}{x + 3}$

$\dfrac{A}{x - 1} + \dfrac{B}{(x - 1)^2} + \dfrac{C}{x + 3}$

$\dfrac{Ax + B}{(x - 1)^2} + \dfrac{C}{x + 3}$

$\dfrac{1}{\sqrt{1 - x^2}}$

$\dfrac{1}{1 + x^2}$

$-\dfrac{1}{1 + x^2}$

$\dfrac{1}{1 - x^2}$

Chain rule only

Quotient rule

Product rule

No rule needed

$\dfrac{dx/dt}{dy/dt}$

$\dfrac{dy/dt}{dx/dt}$

$\dfrac{d^2y/dt^2}{d^2x/dt^2}$

$\dfrac{dy}{dt} \cdot \dfrac{dx}{dt}$

$y = 3x^2$

$y = \sin x$

$y = x^{x}$

$y = e^{2x}$

Substitution

Integration by parts

Partial fractions

A standard result

Exponential, trig, algebra, inverse trig, logs

Logs, inverse trig, algebra, trig, exponential

Algebra, logs, trig, exponential, inverse trig

Trig, exponential, logs, algebra, inverse trig

$\displaystyle\int_a^b y\,dx$

$\displaystyle\pi\int_a^b y\,dx$

$\displaystyle\pi\int_a^b y^2\,dx$

$\displaystyle 2\pi\int_a^b y^2\,dx$

$\dfrac{dy}{dx} + xy = x^2$

$\dfrac{dy}{dx} = xy$

$\dfrac{dy}{dx} + y = e^{2x}$

$\dfrac{d^2y}{dx^2} + y = 0$

$x$

$x^2$

$e^{x}$

$2\ln x$

$m^2 - 5m + 6 = 0$

$m^2 + 5m + 6 = 0$

$5m^2 - 6m = 0$

$m^2 - 6m + 5 = 0$

$Ae^{mx} + Be^{mx}$

$(A + Bx)e^{mx}$

$A\cos mx + B\sin mx$

$Ae^{mx} + Bxe^{2mx}$

$Ae^{\alpha x} + Be^{\beta x}$

$e^{\alpha x}(A\cos\beta x + B\sin\beta x)$

$(A + Bx)e^{\alpha x}$

$A\cos\alpha x + B\sin\beta x$

The complementary function only

The particular integral only

Complementary function plus particular integral

The auxiliary equation